Look for an individual long-term disability policy that can do a temporary group plan offset in your policy and that otherwise converts to the full coverage desired when you cease to be a group member (i.e. you resign from the job or are terminated.)
Essentially, such an individual LTD policy acknowledges you may receive benefits as a member of the existing group LTD plan, yet enhances its benefits. The individual plan would only top up (as opposed to double up) your disability benefits while you are still a group member, and upgrades when you are no longer a member.
I was in a similar situation some years ago. In my case, I had already purchased an individual LTD policy when working as a self-employed IT contractor; I had no group coverage. But, one of the features I selected for the policy was an annual "future income option", guaranteeing I could buy more coverage (without any further medical) as my income would increase. I took advantage of it from time to time since I was younger and my income was growing quickly.
A couple of contract gigs later, I found myself back in a full-time job. The employer enrolled me in their group LTD plan, which was inferior to my individual plan in a number of respects (the definition of disability, wasn't "own occupation" coverage, etc.), so I maintained my individual policy alongside. While employed full time, I was again offered the opportunity to purchase additional coverage based on higher income. When I applied for increased benefits, the application form had this question:
If you have group coverage, would you accept the addition of a group offset amendment, if required, due to your group coverage in force? Yes ___ No ___.
Essentially, I needed to accept the group offset amendment which meant, in effect, "We will increase your individual LTD policy benefits, but as long as you are part of your group LTD plan, those benefits will pay first and reduce additional benefits from your individual plan — until you are no longer part of the group."
When I left that job years later, I contacted my LTD insurer for another increase and also informed them I was no longer covered by the group LTD plan. The group offset amendment was removed from my policy (I was issued a "Policy Change Rider" confirming that) and so all the added benefits I'd applied for converted to "full" benefits on the policy no longer subject to an offset.
So, look for an individual LTD policy that will acknowledge (a) yes, you are part of a group policy, and this means "offsetting", but (b) more important is that you need a guarantee from the individual LTD policy that when you cease to be a member of the group LTD plan, then your benefits in the individual policy convert to what you previously had in both plans combined.
Ask your agent if he inquired about group offsets specifically. IMHO, if your agent doesn't specialize in individual LTD insurance and instead is a "one stop shop", you should consider talking to an agent who knows LTD inside and out.